A thin circular ring of mass M and radius R is rotating

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A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:

1. ωM
  M - 2m
2. ω(M + 2M)
  M
3. ωM
  M + m
4. ω(M - 2m)
  M + 2m

Correct Option: A

In absence of external torque, L = Iω = constant
I₁ω₁ = I_bω₂,I₁ = MR² + 2mR²
(Moment of inertia of a thin circular ring about an axis vertical to its plane = MR²)

∴ ω₂ =	I₁	ω =	M	ω.
	I₂		M + 2m

ωM
M - 2m

ω(M + 2M)
M

ωM
M + m

ω(M - 2m)
M + 2m